Two part answer:
If you do not need to work and interact with this person - don't. Ignore and block her out - as completely as possible. Do not answer any questions. Do not respond to anything she says. Don't answer emails from her. This should help as if this is a bully, getting no reaction will most probably make them stop as it is not a satisfying result.
If, however, you do have to work with this person:
Since your colleague persists in spite of being confronted by you (I assume you have asked her to stop this behaviour during your confrontations), it is time to take this to a higher level.
Talk to your manager - if your manager is also the manager of this person, all the better.
Explain the problem, explain how this behaviour makes the workplace an unpleasant place and that the remarks are unprofessional and demeaning to both yourself and the colleague. Tell your manager that you want this behaviour to stop and explain what you have already done in order to try and stop it.
If your manager agrees with your assessment of the behaviour or that this person is indeed the problem (they may not agree... think about this possibility before moving on). It is possible that for political or professional reasons, they can't do anything, but assuming they can, this will now be their responsibility. You can report future transgressions to your manager, as they happen and hope things will turn to the best.
What you should not do, under any circumstance is engage in reciprocal behaviour - that will just fuel the behaviour of this colleague and will end up in a tit-for-tat escalation.